# Browse Classroom Capsules and Notes

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Displaying 141 - 150 of 1211

A visual proof of the ordering of the means in the title is presented.

For what positive number $x$ is the $x$-th root of $x$ the greatest?

Bernoullis inequality is presented visually.

An arctangent identity is presented visually.

The author presents a simple proof of a special case of Dirichlets celebrated theorem on primes in arithmetic progressions.

Descriptions of the behavior of a family of functions

Solving an expected value problem without using geometric series

In the game of tennis, if the probability that player $A$ wins a point against player $B$ is a constant value $p$, then the probability that $A$ will win a game from deuce is \(p^2/(1 - 2p...

Solving Pell Equations using Fibonacci-like sequences

The author uses elementary geometric methods to calculate the fraction of the area of a soccer ball covered by pentagons.